Accelerating graph mining algorithms via uniform random edge sampling

The seminal works by Karger [13], [14] have shown that one can use Uniform Random Edge (URE) sampling to generate a graph skeleton which accurately approximates all cut-values in the original graph with high probability under some specific assumptions. As such, the random subgraphs resulted from URE sampling can often be used as substitutes for the original graphs in cut/flow-related graph-optimization problems [14]. In this paper, we extend the results of Karger to show that, besides the value (weight) of the cut-set, the weights of four additional types of edge-set, namely, Volume, Association, Complement Volume and Complement Association, are all well-preserved under URE sampling. More importantly, we show that these well-preserved edge-set metrics have dominant impact on the outcome of common graph-mining tasks including PageRank computation and Community Detection. As a result, URE sampling can be used to accelerate the corresponding graph-mining algorithms with small approximation errors. Via extensive experiments with large-scale graphs in practice, we demonstrate that URE sampling can achieve over 90% accuracy for PageRank computation and Modularity-based Community Detection by sampling only 20% edges of the original graph.